Transition metal carbides (TMCs) have been applied in the coatings, molds, and catalysis for their excellent mechanical, thermal, and electrical properties. In this paper, the structural, elastic, thermodynamic and elastic properties of three TMCs (TiC, TaC, and NbC) under pressures were systematically investigated using a firstprinciples calculation. The stability was evaluated by the formation enthalpy, elastic relationship and phonon dispersion. Based on the calculated elastic properties and electronic structure, the thermal conductivity, brittleness, and fracture toughness of TMCs were analyzed. In particular, it is found that the calculated shear modulus and Young modulus of TaC are higher than that of the NbC and TiC. However, the calculated Vickers hardness of TiC is bigger than that of TaC and NbC. Naturally, the high elastic modulus of TMCs is related to the TM-C covalent bond in TM-C layered structure. In addition, the population analysis shows that the bond length of TiC, TaC and NbC are 2.145 & Aring;, 2.197 & Aring; and 2.258 & Aring;, simultaneously with the bond overlap population at 2.07, 2.16 and 2.17, respectively. Furthermore, all of the TMCs exhibit an elastic anisotropy and metallic characteristic. Therefore, we believe that these TMCs not only has excellent mechanical properties, but also has remarkable thermodynamic properties, which can be used in various high-temperature, wear and coating fields.